This script contains code to reproduce statistical analyses and figures for Experiment 1 in the following manuscript:

Rosenbaum, G.M., Grassie, H.L., & Hartley, C.A. (2022). Valence asymmetries in learning account for age differences in risky choice and predict individual differences in subsequent memory. eLife. https://doi.org/10.7554/eLife.64620

Notes

  • Throughout this script, RPE refers to Reward Prediction Error. In the manuscript we use the term Prediction Error (PE) instead
  • The Risk-Sensitive Temporal Difference (RSTD) model is sometimes referred to as “TDRS” in variable names
  • These files include AIC as model-fit metrics. We ultimately reported BIC instead of AIC in the manuscript. This file computes BIC based on AIC values
  • In testing for age patterns in continuous variables, we used the anova function to arbitrate between regression models with linear and quadratic age terms. If the quadratic pattern was significant, we reported the quadratic age pattern; otherwise, we reported the linear age pattern.

Setup

Load Libraries

Load Data

Wide Data

Long Data

Posterior Predictive Check Data

Model Recovery Data

Functions

Demographics

Age: Mean = 17.63, Standard deviation = 5.76

Gender: N males = 30, N females = 32

WASI By Age

Linear age

  WASI
Predictors Estimates CI t df p
(Intercept) 109.71 106.51 – 112.91 68.68 60.00 <0.001
Age_Z -2.07 -5.29 – 1.15 -1.29 60.00 0.203
Observations 62
R2 / R2 adjusted 0.027 / 0.011

Quadratic age

  WASI
Predictors Estimates CI t df p
(Intercept) 108.82 104.00 – 113.64 45.19 59.00 <0.001
Age_Z -2.02 -5.27 – 1.23 -1.25 59.00 0.218
Age_Z^2 0.91 -2.74 – 4.55 0.50 59.00 0.620
Observations 62
R2 / R2 adjusted 0.031 / -0.002

There is no relationship between WASI and linear or quadratic age

Number of Trials

Total number of missed trials across all participants: 37

Maximum number of missed trials for a single participant: 7

Total number of trials (including missed trials): 11346

Accuracy

Test performance

Is quadratic better than linear?

Quadratic is not better, reporting linear results

  TestAccuracy
Predictors z p Odds Ratios CI
(Intercept) 13.21 <0.001 4.28 3.45 – 5.31
TrialNum 8.56 <0.001 2.03 1.72 – 2.38
Age_Z 0.51 0.612 1.06 0.86 – 1.30
TrialNum * Age_Z 0.22 0.830 1.02 0.87 – 1.19
Random Effects
σ2 3.29
τ00 SubjectNumber 0.51
τ11 SubjectNumber.TrialNum 0.20
ρ01 SubjectNumber 0.91
ICC 0.18
N SubjectNumber 62
Observations 2592
Marginal R2 / Conditional R2 0.113 / 0.269

Mean test trial accuracy by block:

Block 1 = 0.63

Block 2 = 0.8

Block 3 = 0.84

Learning curves

Appendix 1–figure 1

Explicit Learning

Question 1: Did this machine always give you the same number of points, or did it sometimes give 0 points and sometimes give you more points?

Mean accuracy = 0.85

Accuracy and age:

Linear age pattern because quadratic isn’t significant:

  RiskySafeAcc
Predictors Estimates CI t df p
(Intercept) 0.85 0.80 – 0.89 37.90 60.00 <0.001
Age_Z -0.02 -0.06 – 0.03 -0.88 60.00 0.382
Observations 62
R2 / R2 adjusted 0.013 / -0.004

Question 2: How many points did this machine give you each time you chose it? (if the participant responded that it was safe in Question 1) OR How many points did this machine give you when it did not give 0 points?

Mean accuracy = 0.84

Accuracy and age:

Linear age pattern because quadratic isn’t significant:

  ValueAcc
Predictors Estimates CI t df p
(Intercept) 0.84 0.79 – 0.90 31.65 60.00 <0.001
Age_Z 0.02 -0.04 – 0.07 0.65 60.00 0.516
Observations 62
R2 / R2 adjusted 0.007 / -0.009

RT

RT cleanup

Total number of RTs removed across all participants: 22

Maximum number for a given participant: 9

Total number of trials with responses (excluding trials with no response): 11309

RT by age

Linear age pattern because quadratic isn’t significant:

  LogRT
Predictors t df p Estimates CI
(Intercept) -8.44 11279.00 <0.001 -0.32 -0.40 – -0.25
TrialNum 1.14 11279.00 0.254 0.01 -0.01 – 0.03
Age_Z -1.07 11279.00 0.283 -0.04 -0.12 – 0.03
TrialNum * Age_Z -2.10 11279.00 0.036 -0.02 -0.04 – -0.00
Random Effects
σ2 0.15
τ00 SubjectNumber 0.09
τ11 SubjectNumber.TrialNum 0.00
ρ01 SubjectNumber -0.17
ICC 0.38
N SubjectNumber 62
Observations 11287
Marginal R2 / Conditional R2 0.009 / 0.388

Risk Taking

Risk descriptive statistics

Equal expected value risk trials

Mean risk taking = 0.37

SD risk taking = 0.21

Was risk taking significantly different than .5 (risk-neutral)?

One Sample t-test: widedf$MeanRiskOverallEqEV
Test statistic df P value Alternative hypothesis mean of x
-4.873 61 8.181e-06 * * * two.sided 0.3729

Yes, risk taking was significantly lower than .5

Risk taking by age regressions

Reporting quadratic because it’s significantly better

  MeanRiskOverallEqEV
Predictors Estimates CI t df p
(Intercept) 0.31 0.24 – 0.39 8.17 59.00 <0.001
Age_Z -0.01 -0.06 – 0.04 -0.44 59.00 0.662
Age_Z^2 0.06 0.00 – 0.12 2.14 59.00 0.036
Observations 62
R2 / R2 adjusted 0.077 / 0.046

Figure 2

Unequal expected value risk trials

Risk taking by age regressions

Reporting quadratic because it’s significantly better

  MeanRiskOverallUnEqEV
Predictors Estimates CI t df p
(Intercept) 0.46 0.36 – 0.56 9.06 59.00 <0.001
Age_Z -0.04 -0.10 – 0.03 -1.03 59.00 0.307
Age_Z^2 0.09 0.01 – 0.16 2.21 59.00 0.031
Observations 62
R2 / R2 adjusted 0.096 / 0.065

Appendix 1–figure 2

Models

Setup

BICs for each model

TD median BIC = 145.35

RSTD median BIC = 131.93

FourLR median BIC = 141.25

Utility median BIC = 131.06

Testing for linear or quadratic age patterns in BIC for each model (none are significant)

TD

  TD_BIC
Predictors Estimates CI t df p
(Intercept) 138.25 124.87 – 151.62 20.67 60.00 <0.001
Age 0.15 -0.57 – 0.87 0.42 60.00 0.679
Observations 62
R2 / R2 adjusted 0.003 / -0.014
  TD_BIC
Predictors Estimates CI t df p
(Intercept) 106.74 66.69 – 146.79 5.33 59.00 <0.001
Age 4.19 -0.71 – 9.09 1.71 59.00 0.092
Age^2 -0.12 -0.25 – 0.02 -1.67 59.00 0.101
Observations 62
R2 / R2 adjusted 0.048 / 0.015

RSTD

  TDRS_BIC
Predictors Estimates CI t df p
(Intercept) 136.58 116.92 – 156.24 13.90 60.00 <0.001
Age -0.50 -1.56 – 0.56 -0.94 60.00 0.350
Observations 62
R2 / R2 adjusted 0.015 / -0.002
  TDRS_BIC
Predictors Estimates CI t df p
(Intercept) 154.80 94.78 – 214.82 5.16 59.00 <0.001
Age -2.84 -10.18 – 4.51 -0.77 59.00 0.443
Age^2 0.07 -0.14 – 0.27 0.64 59.00 0.522
Observations 62
R2 / R2 adjusted 0.021 / -0.012

FourLR

  TDRS_BIC
Predictors Estimates CI t df p
(Intercept) 136.58 116.92 – 156.24 13.90 60.00 <0.001
Age -0.50 -1.56 – 0.56 -0.94 60.00 0.350
Observations 62
R2 / R2 adjusted 0.015 / -0.002
  FourLR_BIC
Predictors Estimates CI t df p
(Intercept) 169.52 105.67 – 233.36 5.31 59.00 <0.001
Age -3.77 -11.58 – 4.05 -0.97 59.00 0.338
Age^2 0.09 -0.13 – 0.31 0.83 59.00 0.407
Observations 62
R2 / R2 adjusted 0.027 / -0.006

Utility

  TDRS_BIC
Predictors Estimates CI t df p
(Intercept) 136.58 116.92 – 156.24 13.90 60.00 <0.001
Age -0.50 -1.56 – 0.56 -0.94 60.00 0.350
Observations 62
R2 / R2 adjusted 0.015 / -0.002
  Util_BIC
Predictors Estimates CI t df p
(Intercept) 166.48 104.53 – 228.43 5.38 59.00 <0.001
Age -4.32 -11.90 – 3.27 -1.14 59.00 0.259
Age^2 0.11 -0.11 – 0.32 0.98 59.00 0.332
Observations 62
R2 / R2 adjusted 0.038 / 0.006

BIC Comparing all 4 models

Appendix 1–figure 5

RSTD vs. TD

Appendix 1–figure 6

Number of participants better fit by TD: 25

Number of participants better fit by RSTD: 37

RSTD vs. Utility

Appendix 1–figure 11A

Median delta BIC - subject level 0.33

Number of participants better fit by Utility: 36

Number of participants better fit by RSTD: 26

RSTD parameter ~ age regressions and plots

Asymetry Index (AI)

Mean AI = -0.22

Standard Deviation of AI = 0.5

Reporting quadratic age effect

  TDRS_AsymmIdx
Predictors Estimates CI t df p
(Intercept) -0.38 -0.57 – -0.20 -4.20 59.00 <0.001
Age_Z -0.06 -0.18 – 0.06 -0.97 59.00 0.338
Age_Z^2 0.17 0.03 – 0.31 2.43 59.00 0.018
Observations 62
R2 / R2 adjusted 0.108 / 0.078

Figure 3

Alpha +

Reporting linear age

  TDRS_AlphaPos
Predictors Estimates CI t df p
(Intercept) 0.21 0.16 – 0.26 8.72 60.00 <0.001
Age_Z -0.02 -0.07 – 0.03 -0.85 60.00 0.401
Observations 62
R2 / R2 adjusted 0.012 / -0.005

Appendix 1–figure 10A

Alpha -

Reporting quadratic age

  TDRS_AlphaNeg
Predictors Estimates CI t df p
(Intercept) 0.43 0.35 – 0.51 10.94 59.00 <0.001
Age_Z -0.00 -0.06 – 0.05 -0.17 59.00 0.869
Age_Z^2 -0.09 -0.15 – -0.03 -3.01 59.00 0.004
Observations 62
R2 / R2 adjusted 0.133 / 0.103

Appendix 1–figure 10B

Beta

Reporting linear age

  TDRS_Beta
Predictors Estimates CI t df p
(Intercept) 5.75 4.98 – 6.52 14.98 60.00 <0.001
Age_Z 0.56 -0.22 – 1.33 1.44 60.00 0.156
Observations 62
R2 / R2 adjusted 0.033 / 0.017

Appendix 1–figure 10C

Learning and agency - FourLR model

Setup

Alpha+ free vs forced

Tests for normality

Shapiro-Wilk normality test: FourLRDF$AlphaPos_Free
Test statistic P value
0.8854 3.061e-05 * * *
Shapiro-Wilk normality test: FourLRDF$AlphaPos_Forced
Test statistic P value
0.8431 1.395e-06 * * *

Not normal, need to run nonparametric test

Wilcoxon signed rank test with continuity correction: FourLRDF$AlphaPos_Free and FourLRDF$AlphaPos_Forced
Test statistic P value Alternative hypothesis
1338 0.01137 * two.sided

Median alpha+ free: 0.22

Median alpha+ forced: 0.14

Appendix 1–figure 12A

Alpha- free vs forced

Tests for normality

Shapiro-Wilk normality test: FourLRDF$AlphaNeg_Free
Test statistic P value
0.9517 0.01609 *
Shapiro-Wilk normality test: FourLRDF$AlphaNeg_Forced
Test statistic P value
0.9313 0.001858 * *

Not normal, need to run nonparametric test

Wilcoxon signed rank test with continuity correction: FourLRDF$AlphaNeg_Free and FourLRDF$AlphaNeg_Forced
Test statistic P value Alternative hypothesis
794 0.202 two.sided

Median alpha- free: 0.35

Median alpha- forced: 0.32

Appendix 1–figure 12B

AI free vs forced

Tests for normality

Shapiro-Wilk normality test: FourLRDF$AI_Free
Test statistic P value
0.9482 0.01097 *
Shapiro-Wilk normality test: FourLRDF$AI_Forced
Test statistic P value
0.927 0.001204 * *

Not normal, need to run nonparametric test

Wilcoxon signed rank test with continuity correction: FourLRDF$AI_Free and FourLRDF$AI_Forced
Test statistic P value Alternative hypothesis
1377 0.005041 * * two.sided

Median AI free: -0.12

Median AI forced: -0.39

Appendix 1–figure 12C

Memory

Memory Summary Stats

Hit Rate:

Mean = 0.54 SD = 0.14

False Alarm Rate:

Mean = 0.24 SD = 0.15

d’:

Mean = 0.93 SD = 0.48

Memory after risky vs. safe

Do the distributions for memory after risky or safe hits deviate significantly from normality?

Shapiro-Wilk normality test: RiskySafeHitswide$Risky
Test statistic P value
0.9881 0.8097
Shapiro-Wilk normality test: RiskySafeHitswide$Safe
Test statistic P value
0.9807 0.438

No, they don’t; distributions are normal

Hits after risky choices:

Mean = 0.56 SD = 0.15

Hits after safe choices:

Mean = 0.52 SD = 0.15

Did memory significantly differ after risky vs. safe choices?

Paired t-test: RiskySafeHitswide$Risky and RiskySafeHitswide$Safe (continued below)
Test statistic df P value Alternative hypothesis
3.077 61 0.003126 * * two.sided
mean of the differences
0.03287

Yes, memory was better for images presented after risky vs. safe choices

Memory performance by age - summary stats

Hits:

Reporting linear age

  Hit
Predictors Estimates CI t df p
(Intercept) 0.54 0.50 – 0.57 30.16 60.00 <0.001
Age_Z 0.03 -0.01 – 0.06 1.47 60.00 0.146
Observations 62
R2 / R2 adjusted 0.035 / 0.019

False Alarms:

Reporting linear age

  FA
Predictors Estimates CI t df p
(Intercept) 0.24 0.20 – 0.27 12.79 60.00 <0.001
Age_Z 0.04 0.00 – 0.08 2.13 60.00 0.037
Observations 62
R2 / R2 adjusted 0.070 / 0.055

Appendix 1–figure 3A

d’

Reporting linear age

  dPrime
Predictors Estimates CI t df p
(Intercept) 0.93 0.81 – 1.05 15.50 60.00 <0.001
Age_Z -0.11 -0.23 – 0.01 -1.84 60.00 0.070
Observations 62
R2 / R2 adjusted 0.054 / 0.038

Appendix 1–figure 3B

Learning and Memory

Memory Mixed Effects Regression - RSTD

Setup

Model

  RespOld
Predictors z p Odds Ratios CI
(Intercept) 1.45 0.147 1.17 0.94 – 1.46
AIScale -0.68 0.498 0.95 0.82 – 1.10
AbsRPEScale 4.75 <0.001 1.19 1.11 – 1.28
PositiveRPEC -1.61 0.108 0.93 0.86 – 1.02
MemIdxScaled -5.83 <0.001 0.82 0.76 – 0.87
Age_Z 0.32 0.750 1.02 0.89 – 1.17
Age_Z^2 -0.18 0.856 0.99 0.84 – 1.15
FAScale 4.86 <0.001 1.41 1.23 – 1.61
AIScale * AbsRPEScale 0.43 0.664 1.01 0.96 – 1.07
AIScale * PositiveRPEC 1.94 0.052 1.07 1.00 – 1.15
AbsRPEScale *
PositiveRPEC 		-0.15 0.878 0.99 0.93 – 1.07
(AIScale * AbsRPEScale) *
PositiveRPEC 		3.45 0.001 1.12 1.05 – 1.19
Random Effects
σ2 3.29
τ00 SubjectNumber 0.25
τ11 SubjectNumber.AbsRPEScale 0.01
τ11 SubjectNumber.MemIdxScaled 0.05
ρ01  
ρ01  
ICC 0.07
N SubjectNumber 62
Observations 11309
Marginal R2 / Conditional R2 0.049 / 0.115

Plot

Figure 4a

Figure 4b

Appendix 1–figure 13C (same as 4b but with a different title and no legend)

Memory Mixed Effects + Forced variable (appendix)

Model

Including Forced as a covariate

  RespOld
Predictors z p Odds Ratios CI
(Intercept) 1.45 0.147 1.17 0.95 – 1.46
AIScale -0.69 0.489 0.95 0.82 – 1.10
AbsRPEScale 4.71 <0.001 1.19 1.11 – 1.28
PositiveRPEC -1.59 0.113 0.93 0.86 – 1.02
ForcedC -0.44 0.664 0.99 0.95 – 1.04
MemIdxScaled -5.83 <0.001 0.82 0.76 – 0.87
Age_Z 0.32 0.746 1.02 0.89 – 1.17
Age_Z^2 -0.18 0.856 0.99 0.84 – 1.15
FAScale 4.87 <0.001 1.41 1.23 – 1.61
AIScale * AbsRPEScale 0.39 0.694 1.01 0.95 – 1.07
AIScale * PositiveRPEC 1.92 0.055 1.07 1.00 – 1.15
AbsRPEScale *
PositiveRPEC 		-0.22 0.827 0.99 0.93 – 1.06
(AIScale * AbsRPEScale) *
PositiveRPEC 		3.44 0.001 1.12 1.05 – 1.19
Random Effects
σ2 3.29
τ00 SubjectNumber 0.25
τ11 SubjectNumber.AbsRPEScale 0.01
τ11 SubjectNumber.MemIdxScaled 0.05
τ11 SubjectNumber.ForcedC 0.01
ρ01  
ρ01  
ICC 0.07
N SubjectNumber 62
Observations 11309
Marginal R2 / Conditional R2 0.049 / 0.115

4-way interaction with forced variable

  RespOld
Predictors z p Odds Ratios CI
(Intercept) 0.67 0.504 1.08 0.86 – 1.37
AsymmIdx -0.71 0.477 0.90 0.66 – 1.21
AbsRPE 3.55 <0.001 1.78 1.29 – 2.44
PositiveRPE [Positive
Prediction Error] 		-0.53 0.593 0.92 0.69 – 1.24
Forced [1] -0.22 0.823 0.99 0.87 – 1.12
MemIdxScaled -5.81 <0.001 0.82 0.76 – 0.88
Age_Z 0.30 0.765 1.02 0.89 – 1.17
Age_Z^2 -0.16 0.873 0.99 0.84 – 1.15
FAScale 4.95 <0.001 1.41 1.23 – 1.62
AsymmIdx * AbsRPE -2.28 0.023 0.47 0.25 – 0.90
AsymmIdx * PositiveRPE
[Positive Prediction
Error] 		-1.22 0.221 0.73 0.44 – 1.21
AbsRPE * PositiveRPE
[Positive Prediction
Error] 		0.60 0.550 1.24 0.61 – 2.54
AsymmIdx * Forced [1] 0.28 0.777 1.03 0.83 – 1.28
AbsRPE * Forced [1] -0.49 0.626 0.88 0.53 – 1.46
PositiveRPE [Positive
Prediction Error] *
Forced [1] 		-0.46 0.643 0.90 0.58 – 1.40
(AsymmIdx * AbsRPE) *
PositiveRPE [Positive
Prediction Error] 		3.84 <0.001 10.79 3.21 – 36.35
(AsymmIdx * AbsRPE) *
Forced [1] 		-0.24 0.811 0.89 0.34 – 2.33
(AsymmIdx * PositiveRPE
[Positive Prediction
Error]) * Forced [1] 		1.53 0.125 1.78 0.85 – 3.70
(AbsRPE * PositiveRPE
[Positive Prediction
Error]) * Forced [1] 		0.38 0.704 1.25 0.40 – 3.89
(AsymmIdx * AbsRPE
PositiveRPE [Positive
Prediction Error])
Forced [1] 		-1.49 0.135 0.27 0.05 – 1.51
Random Effects
σ2 3.29
τ00 SubjectNumber 0.24
τ11 SubjectNumber.AbsRPE 0.10
τ11 SubjectNumber.MemIdxScaled 0.05
ρ01  
ρ01  
ICC 0.07
N SubjectNumber 62
Observations 11309
Marginal R2 / Conditional R2 0.050 / 0.116

Plot

Appendix 1–figure 13A

Appendix 1–figure 13B

Memory Mixed Effects Regression - risky only

  RespOld
Predictors z p Odds Ratios CI
(Intercept) 1.60 0.109 1.22 0.96 – 1.56
AIScale -0.23 0.815 0.98 0.83 – 1.16
AbsRPEScale 2.22 0.026 1.11 1.01 – 1.23
PositiveRPEC -2.26 0.024 0.89 0.80 – 0.98
MemIdxScaled -4.21 <0.001 0.83 0.76 – 0.90
Age_Z 0.33 0.743 1.03 0.88 – 1.20
Age_Z^2 0.02 0.983 1.00 0.84 – 1.20
FAScale 3.88 <0.001 1.36 1.16 – 1.59
AIScale * AbsRPEScale 0.40 0.689 1.01 0.95 – 1.08
AIScale * PositiveRPEC 0.63 0.529 1.03 0.94 – 1.14
AbsRPEScale *
PositiveRPEC 		1.14 0.256 1.05 0.96 – 1.16
(AIScale * AbsRPEScale) *
PositiveRPEC 		2.34 0.019 1.11 1.02 – 1.21
Random Effects
σ2 3.29
τ00 SubjectNumber 0.28
τ11 SubjectNumber.AbsRPEScale 0.00
τ11 SubjectNumber.MemIdxScaled 0.06
ρ01  
ρ01  
ICC 0.08
N SubjectNumber 62
Observations 4625
Marginal R2 / Conditional R2 0.044 / 0.120

Ordinal regression - confidence in memory

Model

Appendix 1–Table 1

  RespOrdinalflip
Predictors z p Odds Ratios CI
Definitely New|Maybe New -10.56 <0.001 0.25 0.19 – 0.32
Maybe New|Maybe Old -1.42 0.156 0.83 0.64 – 1.07
Maybe Old|Definitely Old 4.75 <0.001 1.86 1.44 – 2.40
AIScale 0.11 0.915 1.01 0.85 – 1.20
AbsRPEScale 6.20 <0.001 1.24 1.16 – 1.33
PositiveRPEC -2.38 0.017 0.91 0.84 – 0.98
MemIdxScaled -6.21 <0.001 0.81 0.75 – 0.86
Age_Z 0.41 0.685 1.03 0.88 – 1.22
Age_Z^2 -1.07 0.286 0.90 0.74 – 1.09
FAScale 4.90 <0.001 1.55 1.30 – 1.85
AIScale * AbsRPEScale -0.01 0.993 1.00 0.95 – 1.05
AIScale * PositiveRPEC 3.08 0.002 1.10 1.04 – 1.17
AbsRPEScale *
PositiveRPEC 		-0.13 0.897 1.00 0.94 – 1.06
(AIScale * AbsRPEScale) *
PositiveRPEC 		3.65 <0.001 1.11 1.05 – 1.17
Random Effects
σ2 3.29
τ00 SubjectNumber 0.37
τ11 SubjectNumber.AbsRPEScale 0.01
τ11 SubjectNumber.MemIdxScaled 0.06
ρ01 -0.04
-0.05
ICC 0.12
N SubjectNumber 62
Observations 11309
Marginal R2 / Conditional R2 0.067 / 0.175

Plot

Appendix 1–figure 4

Utility + memory

  RespOld
Predictors z p Odds Ratios CI
(Intercept) 1.20 0.229 1.16 0.91 – 1.47
RhoScale -0.25 0.800 0.98 0.83 – 1.16
AbsRPEScale -0.36 0.715 0.84 0.32 – 2.17
PositiveRPEC -0.49 0.627 0.97 0.86 – 1.09
MemIdxScaled -5.85 <0.001 0.82 0.76 – 0.87
Age_Z 0.33 0.745 1.02 0.89 – 1.17
Age_Z^2 0.00 0.997 1.00 0.86 – 1.17
FAScale 4.82 <0.001 1.40 1.22 – 1.61
RhoScale * AbsRPEScale 0.36 0.717 1.07 0.74 – 1.54
RhoScale * PositiveRPEC 1.21 0.227 1.06 0.96 – 1.17
AbsRPEScale *
PositiveRPEC 		-1.06 0.291 0.65 0.29 – 1.45
(RhoScale * AbsRPEScale)
* PositiveRPEC 		1.06 0.291 1.18 0.87 – 1.60
Random Effects
σ2 3.29
τ00 SubjectNumber 0.25
τ11 SubjectNumber.MemIdxScaled 0.05
ρ01  
ρ01  
ICC 0.07
N SubjectNumber 62
Observations 11309
Marginal R2 / Conditional R2 0.045 / 0.112

Relationship between Utility and RSTD RPEs

Setup

Plots

Relationship between RSTD and utility RPEs for all participants:

Appendix 1–Figure 11B

Relationship between RSTD and utility RPEs for 2 representative participants:

Appendix 1–figure 11C

Appendix 1–figure 11D

Appendix 1–figure 11E

Appendix 1–figure 11F

DOSPERT

Model

Reporting quadratic effect

  DOSPERT_rs
Predictors Estimates CI t df p
(Intercept) 4.17 3.81 – 4.53 23.31 59.00 <0.001
Age_Z 0.15 -0.09 – 0.39 1.27 59.00 0.208
Age_Z^2 -0.42 -0.69 – -0.15 -3.09 59.00 0.003
Observations 62
R2 / R2 adjusted 0.166 / 0.137

Plot

Figure 5

Task and self-reported risk taking

  DOSPERT_rs
Predictors Estimates CI t df p
(Intercept) 4.01 3.42 – 4.60 13.58 60.00 <0.001
MeanRiskAll -0.58 -1.80 – 0.64 -0.95 60.00 0.347
Observations 62
R2 / R2 adjusted 0.015 / -0.002

Correlation between DOSPERT score and task risk taking:

Pearson’s product-moment correlation: widedf$DOSPERT_rs and widedf$MeanRiskAll
Test statistic df P value Alternative hypothesis cor
-0.9478 60 0.347 two.sided -0.1215

95% CI of correlation: -0.3603 and 0.1323

Posterior Predictive Check

RSTD

Model

  MeanRiskOverallEqEV_sim
Predictors Estimates CI t df p
(Intercept) 0.35 0.28 – 0.41 10.70 59.00 <0.001
Age_Z -0.02 -0.07 – 0.02 -1.02 59.00 0.310
Age_Z^2 0.05 0.00 – 0.10 2.16 59.00 0.035
Observations 62
R2 / R2 adjusted 0.093 / 0.062

Correlation between risk taking in simulated vs real data:

Pearson’s product-moment correlation: PPC_RealData$MeanRiskOverallEqEV_sim and PPC_RealData$MeanRiskOverallEqEV
Test statistic df P value Alternative hypothesis cor
18.14 60 4.846e-26 * * * two.sided 0.9197

95% CI of correlation: 0.8697 and 0.951

Plots

Appendix 1–figure 9A

Appendix 1–figure 9B

Utility

Model

  MeanRiskOverallEqEV_sim
Predictors Estimates CI t df p
(Intercept) 0.34 0.28 – 0.40 11.15 59.00 <0.001
Age_Z -0.02 -0.06 – 0.02 -0.97 59.00 0.336
Age_Z^2 0.05 0.01 – 0.10 2.29 59.00 0.026
Observations 62
R2 / R2 adjusted 0.099 / 0.068

Correlation between risk taking in simulated vs real data:

Pearson’s product-moment correlation: PPC_Util_RealData$MeanRiskOverallEqEV_sim and PPC_Util_RealData$MeanRiskOverallEqEV
Test statistic df P value Alternative hypothesis cor
15.25 60 2.579e-22 * * * two.sided 0.8916

95% CI of correlation: 0.8258 and 0.9335

Plots

Appendix 1–figure 9C

Appendix 1–figure 9D

Comparing PPCs in TDRS/Util

  • Call: r.test(n = 62 , r12 = 0.919695175096668 , r23 = 0.977264014393715 , r13 = 0.891630174175368 )

  • Test: Test of difference between two correlated correlations

  • t:

    cor
    2.583

  • p:

    cor
    0.01228

Model Recovery

Setup

RSTD vs. TD Model Recovery

Appendix 1–figure 7

Model recovery table

Table 2

GenMod TD RSTD FourLR Util
TD NA 0.98 1.00 0.97
RSTD 0.57 NA 0.99 0.65
FourLR 0.50 0.31 NA 0.39
Util 0.58 0.76 0.99 NA

Parameter recoverability

Recoverability values are the correlation between the real parameter values and the recovered parameter values. Recoverability is reported in Table 1.

TD

Alpha: 0.84

Beta: 0.88

RSTD

Alpha +: 0.79

Alpha -: 0.88

Beta: 0.9

FourLR

Alpha + Free: 0.79

Alpha - Free: 0.89

Alpha + Forced: 0.76

Alpha - Forced: 0.78

Beta: 0.9

Utility

Alpha: 0.75

Beta: 0.88

Rho: 0.88

RSTD Binned Parameter Recovery

Make bins

AILevel meanAI minAI maxAI
Low AI -0.60810915 -0.93911096 -0.37404138
Medium-Low AI -0.21416440 -0.37398264 -0.07684006
Medium-High AI 0.06933452 -0.07682883 0.25012080
High AI 0.54818146 0.25039525 0.96950198

Plot

Appendix 1–figure 8A

Appendix 1–figure 8B

Appendix 1–figure 8C

Appendix 1–figure 8D

Percent of real participants with AIs in lower 3 quadrants: 0.8064516

RSTD Binned parameter Recovery - subset with beta > 2 (referenced in Appendix 1)